About Operation Unthinkable:
I really don't think that it should be a battle scenario. The scope is the worldmap, and it would entice multiple battles.
Militarily, it would have been a disaster for the Allies. The Russians were at their best, experienced troops and better weapons overall. They would have crushed them.
The atomic bomb barely would have played any role in the conflict... what would the Americans have used it on? Most Russians cities were already thoroughly destroyed after the war, with all industry dispersed far inland. Also, the bombs available in 1945, 1946 were much too weak to cause any damage to real cities. European cities are made of stone, not wood and paper like the Japanese houses. The only target would have been Moskva, and I doubt the Allied bombers would have been able to reach that. And if they did, they would've levelled one or two suburbs or boroughs, at best. Bombing troop concentrations would have been useless, what's another 100k casualties for the Russians?
As to how WWIII would have started: Probably the only person who seriously contemplated a war between the Allies and Russia was Stalin himself. What was to stop him from taking more of Germany? Or France, for that matter? Don't think that the Russians had forgotten that the French had tried to conquer them 150 years earlier. Crushing the one million Allied soldiers on the mainland would have been a piece of cake with the millions that he had under arms. It makes you wonder why he stopped. The Allies pretty much tried to appease him, basically giving him everything he wanted (half of Poland!), they even sent people to him to get massacred. Don't think they didn't know what they were doing..